Question

which notation describes this transformation?
a. $(x,y)=(-x,y)$
b. $(x,y)=(x - 9,y + 2)$
c. $(x,y)=(-y,x)$
d. $(x,y)=(x + 9,y - 2)$

Explanation:

Step1: Analyze each option

• Option A: \((x',y')=(-x,y)\) represents a reflection over the \(y -\)axis.
• Option B: \((x',y')=(x - 9,y + 2)\) represents a translation \(9\) units to the left and \(2\) units up.
• Option C: \((x',y')=(-y,x)\) represents a rotation.
• Option D: \((x',y')=(x + 9,y - 2)\) represents a translation.

Step2: Check the translation

Let's take a point from figure \(1\) and figure \(2\). Suppose a vertex of figure \(1\) is \((5,-3)\) and a corresponding vertex of figure \(2\) is \((-4,-1)\).
If we use the transformation \((x',y')=(x - 9,y + 2)\):
For \(x = 5\), \(x'=5-9=-4\); for \(y=-3\), \(y'=-3 + 2=-1\)

Answer:

B. \((x',y')=(x - 9,y + 2)\)